Decomposing cubic bèzier segments for tessellation-free stencil filling

ABSTRACT

One embodiment of the present invention sets forth a technique for decomposing and filling cubic Bèzier segments of paths without tessellating the paths. Path rendering may be accelerated when a GPU or other processor is configured to perform the decomposition operations. Cubic Bèzier paths are classified and decomposed into simple cubic Bèzier path segments based on the classification. A stencil buffer is then generated that indicates pixels that are inside of the decomposed cubic Bèzier segments. The paths are then filled according to the stencil buffer to produce a filled path.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority benefit to United States provisionalpatent application titled, “Path Rendering,” filed on May 21, 2010 andhaving Ser. No. 61/347,359 (Attorney Docket Number NVDA/SC-10-0110-US0).This related application is also hereby incorporated by reference in itsentirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to graphics processing and morespecifically to decomposing cubic Bèzier segments for tessellation-freestencil filling.

2. Description of the Related Art

Path rendering is a style of resolution-independent two-dimensional (2D)rendering, often called “vector graphics,” that is the basis for anumber of important rendering standards such as PostScript, Java 2D,Apple's Quartz 2D, OpenVG, PDF, TrueType fonts, OpenType fonts,PostScript fonts, Scalable Vector Graphics (SVG) web format, Microsoft'sSilverlight and Adobe Flash for interactive web experiences, Microsoft'sSML Paper Specification (XPS), drawings in Office file formats includingPowerPoint, Adobe Illustrator illustrations, and more.

Path rendering is resolution-independent meaning that a scene isdescribed by paths without regard to the pixel resolution of theframebuffer. This is in contrast to the resolution-dependent nature ofso-called bitmapped graphics. Whereas bitmapped images exhibit blurredor pixilated appearance when zoomed or otherwise transformed, scenesspecified with path rendering can be rendered at different resolutionsor otherwise transformed without blurring the boundaries of filled orstroked paths.

Sometimes the term vector graphics is used to mean path rendering, butpath rendering is a more specific approach to computer graphics. Whilevector graphics could be any computer graphics approach that representsobjects (typically 2D) in a resolution-independent way, path renderingis a much more specific rendering model with salient features thatinclude path filling, path stroking, path masking, compositing, and pathsegments specified as Bèzier curves.

FIG. 1A is a prior art scene composed of a sequence of paths. In pathrendering, a 2D picture or scene such as that shown in FIG. 1A isspecified as a sequence of paths. Each path is specified by a sequenceof path commands and a corresponding set of scalar coordinates. Pathrendering is analogous to how an artist draws with pens and brushes. Apath is a collection of sub-paths. Each sub-path (also called atrajectory) is a connected sequence of line segments and/or curvedsegments. Each sub-path may be closed, meaning the sub-path's start andterminal points are the same location so the stroke forms a loop;alternatively, a sub-path can be open, meaning the sub-path's start andterminal points are distinct.

When rendering a particular path, the path may be filled, stroked, orboth. As shown in FIG. 1A, the paths constituting the scene are stroked.When a path is both filled and stroked, typically the stroking operationis done immediately subsequent to the filling operation so the strokingoutlines the filled region. Artists tend to use stroking and fillingtogether in this way to help highlight or offset the filled region sotypically the stroking is done with a different color than the filling.

FIG. 1B is the sequence of paths shown in FIG. 1A with only filling.Filling is the process of coloring or painting the set of pixels“inside” the closed sub-paths of a path. Filling is similar to the way achild would “color in between the lines” of a coloring book. If asub-path within a path is not closed when such a sub-path is filled, thestandard practice is to force the sub-path closed by connecting its endand start points with an implicit line segment, thereby closing thesub-path, and then filling that resulting closed path.

While the meaning of “inside a path” generally matches the intuitivemeaning of this phrase, path rendering formalizes this notion with whatis called a fill-rule. The intuitive sense of “inside” is sufficient aslong as a closed sub-path does not self-intersect itself. However if asub-path intersects itself or another sub-path or some sub-paths arefully contained within other sub-paths, what it means to be inside oroutside the path needs to be better specified.

Stroking is distinct from filling and is more analogous to tracing oroutlining each sub-path in a path as if with a pen or marker. Strokingoperates on the perimeter or boundary defined by the path whereasfilling operates on the path's interior. Unlike filling, there is norequirement for the sub-paths within a path to be closed for stroking.For example, the curve of a letter “S” could be stroked without havingto be closed though the curve of the letter “O” could also be stroked.

FIG. 1C is a prior art scene composed of the sequence of paths from FIG.1A with the stroking from FIG. 1A and the filling from FIG. 1B. FIG. 1Cshows how filling and stroking are typically combined in a pathrendering scene for a complete the scene. Both stroking and filling areintegral to the scene's appearance.

Traditionally, graphics processing units (CPUs) have been includedfeatures to accelerate 2D bitmapped graphics and three-dimensional (3D)graphics. In today's systems, nearly all path rendering is performed bya central processing unit (CPU) performing scan-line rendering with noacceleration by a GPU. GPUs do not directly render curved primitives sopath rendering primitives such as Bèzier segments and partial ellipticalarcs must be approximated by lots of tiny triangles when a GPU is usedto render the paths. Constructing the required tessellations of pathapproximated by lots of short connected line segments can create asubstantial CPU burden. The triangles or other polygons resulting fromtessellation are then rendered by the GPU. Because GPUs are so fast atrasterizing triangles, tessellating paths into polygons that can then berendered by GPUs is an obvious approach to GPU-accelerating pathrendering.

Tessellation is a fragile, often quite sequential, process that requiresglobal inspection of the entire path. Tessellation depends on dynamicdata structures to sort, search, and otherwise juggle the incrementalsteps involved in generating a tessellation. Path rendering makes thisprocess considerably harder by permitting curved path segments as wellas allowing path segments to self-intersect, form high genus topologies,and be unbounded in size.

A general problem with using a GPU to render paths is unacceptably poorantialiasing quality when compared to standard CPU-based methods. Theproblem is that GPUs rely on point sampling for rasterization oftriangular primitives with only 1 to 8 samples (often 4) per pixel.CPU-based scan-line methods typically rely on 16 or more samples perpixel and can accumulate coverage over horizontal spans.

Animating or editing paths is costly because it requires re-tessellatingthe entire path since the tessellation is resolution dependent, and ingeneral it is very difficult to prove a local edit to a path will notcause a global change in the tessellation of the path. Furthermore, whencurved path segments are present and the scaling of the path withrespect to pixel space changes appreciably (zooming in say), the curvedpath segments may need to be re-subdivided and re-tessellation is likelyto be necessary.

Additionally, compositing in path rendering systems typically requiresthat pixels rasterized by a filled or stroked path are updatedonce-and-only-once per rasterization of the path. This requirement meansnon-overlapping tessellations are required. So for example, a crosscannot be tessellated as two overlapping rectangles but rather must berendered by the outline of the cross, introducing additional verticesand primitives. In particular, this means the sub-paths of a path cannotbe processed separately without first determining that no two sub-pathsoverlap. These requirements, combined with the generally fragile andsequential nature of tessellation algorithms make path tessellationparticularly expensive. Because of the expense required in generatingtessellations, it is very tempting and pragmatic to cache tessellations.Unfortunately such tessellations are much less compact than the originalpath representations, particularly when curved path segments areinvolved. Consequently, a greater amount of data must be stored to cachepaths after tessellation compared with storing the paths prior totessellation. Such cached tessellations are ineffective when paths areanimated or rendered just once.

Accordingly, what is needed in the art is a robust and efficient systemand method for decomposing and filling cubic Bèzier segments of pathswithout tessellating the paths. Today path filling algorithms execute onthe CPU and are typically implemented in the context of a scan-linerasterizer; these algorithms do not benefit from the efficient executionmodel of the GPU. Tessellating filled paths into triangles for GPUrendering is unattractive for the reasons previously outlined. Atechnique developed by Charles Loop and Jim Blinn (described inResolution Independent Curve Rendering using Programmable GraphicsHardware, ACM Transactions on Graphics, Volume 24, Issue 3, July 2005)provide an implicit form for cubic Bèzier curves suitable for efficientevaluation by pixel shaders, but the technique requires the interior ofthe cubic Bèzier curves to be tessellated into triangles. Otherconventional techniques fill paths without tessellation by renderingconcave polygons constructed of line segments that are not curved usinga stencil buffer. Kokojima et al. (in Resolution Independent Renderingof Deformable Vector Objects using Graphics Hardware, ACM SIGGRAPH 2006Sketches) describe a tessellation-free approach to filling pathsincluding quadratic Bèzier path segments. However, the approachdescribed by Kokojima et al. is limited to quadratic Bèzier curves andthereby avoid the technical difficulties created by the topologicalcomplexity of cubic Bèzier curves. Rueda et. al. (in GPU-based renderingof curved polygons using simplicial coverings. Computers and Graphics,Volume 32, Issue 5, October 2008, pages 581-588.) propose atessellation-free approach capable of handling cubic Bèzier curves.However, their technique requires Bèzier normalization that results inmany times more arithmetic operations per Bèzier curve tested against apoint compared with the implicit form of the Bèzier curve developed byLoop and Blinn. Therefore the present invention develops a method andsystem for decomposing and filling cubic Bèzier segments of paths thatis robust in the face of topological variety of cubic Bèzier curves,inexpensive to evaluate using a programmable GPU, and does nottessellate the interior of the curve, i.e., is free of tessellation.

SUMMARY OF THE INVENTION

One embodiment of the present invention sets forth a technique fordecomposing and filling cubic Bèzier segments of paths withouttessellating the paths. Path rendering may be accelerated when a GPU orother processor that is configured to perform the decompositionoperations. Cubic Bèzier paths are classified and decomposed into simplecubic Bèzier path segments based on the classification. A stencil bufferis then generated that indicates pixels that are inside of thedecomposed cubic Bèzier segments. The paths are then filled according tothe stencil buffer to produce a filled path.

Various embodiments of a method of the invention for decomposing cubicBèzier segments for tessellation-free stencil filling include receivinga path including a cubic Bèzier path segment and subdividing the cubicBèzier path segment into simple cubic Bèzier path segments when thecubic Bèzier path segment is classified as having a serpentine or looptopology. Texture map coordinates are assigned to vertices of the simplecubic Bèzier path segments that define a convex hull geometry and astencil buffer indicating pixels that are inside of the cubic Bèzierpath segment is generated by processing the texture map coordinates.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention can be understood in detail, a more particular description ofthe invention, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1A is a prior art scene composed of a sequence of paths;

FIG. 1B is the fill for the prior art scene shown in FIG. 1A;

FIG. 1C is the prior art scene of FIG. 1A with the fill of FIG. 1B andthe stroked sequence of paths;

FIG. 2A is a block diagram illustrating a computer system configured toimplement one or more aspects of the present invention;

FIG. 2B is a block diagram of a parallel processing subsystem for thecomputer system of FIG. 2A, according to one embodiment of the presentinvention;

FIG. 3A is a block diagram of a GPC within one of the PPUs of FIG. 2B,according to one embodiment of the present invention;

FIG. 3B is a block diagram of a partition unit within one of the PPUs ofFIG. 2B, according to one embodiment of the present invention;

FIG. 3C is a block diagram of a portion of the SPM of FIG. 3A, accordingto one embodiment of the present invention;

FIG. 4 is a conceptual diagram of a graphics processing pipeline thatone or more of the PPUs of FIG. 2B can be configured to implement,according to one embodiment of the present invention;

FIGS. 5A, 5B, 5C, and 5D illustrate paths that are simple Bèzier cubicpath segments, according to one embodiment of the invention;

FIGS. 6A and 6B illustrate paths that are Bèzier cubic path segmentsthat are self-intersecting to form a loop with one root, according toone embodiment of the invention;

FIGS. 6C and 6D illustrate paths that are Bèzier cubic path segmentsthat are self-intersecting to form a loop with two roots, according toone embodiment of the invention;

FIGS. 7A and 7B illustrate paths that are Bèzier cubic path segmentsthat intersect a base line to form a serpentine, according to oneembodiment of the invention;

FIG. 8A is a flow diagram of method steps for decomposing cubic Bèziersegments for tessellation-free stencil filling, according to oneembodiment of the present invention; and

FIG. 8B is a flow diagram of method steps for classifying and processinga cubic path segment as performed in a method step shown in FIG. 8A,according to one embodiment of the present invention.

DETAILED DESCRIPTION

In the following description, numerous specific details are set forth toprovide a more thorough understanding of the present invention. However,it will be apparent to one of skill in the art that the presentinvention may be practiced without one or more of these specificdetails. In other instances, well-known features have not been describedin order to avoid obscuring the present invention.

System Overview

FIG. 2A is a block diagram illustrating a computer system 100 configuredto implement one or more aspects of the present invention. Computersystem 100 includes a central processing unit (CPU) 102 and a systemmemory 104 communicating via an interconnection path that may include amemory bridge 105. Memory bridge 105, which may be, e.g., a Northbridgechip, is connected via a bus or other communication path 106 (e.g., aHyperTransport link) to an I/O (input/output) bridge 107. I/O bridge107, which may be, e.g., a Southbridge chip, receives user input fromone or more user input devices 108 (e.g., keyboard, mouse) and forwardsthe input to CPU 102 via path 106 and memory bridge 105. A parallelprocessing subsystem 112 is coupled to memory bridge 105 via a bus orother communication path 113 (e.g., a PCI Express, Accelerated GraphicsPort, or HyperTransport link); in one embodiment parallel processingsubsystem 112 is a graphics subsystem that delivers pixels to a displaydevice 110 (e.g., a conventional CRT or LCD based monitor). A systemdisk 114 is also connected to I/O bridge 107. A switch 116 providesconnections between I/O bridge 107 and other components such as anetwork adapter 118 and various add-in cards 120 and 121. Othercomponents (not explicitly shown), including USB or other portconnections, CD drives, DVD drives, film recording devices, and thelike, may also be connected to I/O bridge 107. Communication pathsinterconnecting the various components in FIG. 2A may be implementedusing any suitable protocols, such as PCI (Peripheral ComponentInterconnect), PCI-Express, AGP (Accelerated Graphics Port),HyperTransport, or any other bus or point-to-point communicationprotocol(s), and connections between different devices may use differentprotocols as is known in the art.

In one embodiment, the parallel processing subsystem 112 incorporatescircuitry optimized for graphics and video processing, including, forexample, video output circuitry, and constitutes a graphics processingunit (GPU). In another embodiment, the parallel processing subsystem 112incorporates circuitry optimized for general purpose processing, whilepreserving the underlying computational architecture, described ingreater detail herein. In yet another embodiment, the parallelprocessing subsystem 112 may be integrated with one or more other systemelements, such as the memory bridge 105, CPU 102, and I/O bridge 107 toform a system on chip (SoC).

It will be appreciated that the system shown herein is illustrative andthat variations and modifications are possible. The connection topology,including the number and arrangement of bridges, the number of CPUs 102,and the number of parallel processing subsystems 112, may be modified asdesired. For instance, in some embodiments, system memory 104 isconnected to CPU 102 directly rather than through a bridge, and otherdevices communicate with system memory 104 via memory bridge 105 and CPU102. In other alternative topologies, parallel processing subsystem 112is connected to I/O bridge 107 or directly to CPU 102, rather than tomemory bridge 105. In still other embodiments, I/O bridge 107 and memorybridge 105 might be integrated into a single chip. Large embodiments mayinclude two or more CPUs 102 and two or more parallel processing systems112. The particular components shown herein are optional; for instance,any number of add-in cards or peripheral devices might be supported. Insome embodiments, switch 116 is eliminated, and network adapter 118 andadd-in cards 120, 121 connect directly to I/O bridge 107.

FIG. 2B illustrates a parallel processing subsystem 112, according toone embodiment of the present invention. As shown, parallel processingsubsystem 112 includes one or more parallel processing units (PPUs) 202,each of which is coupled to a local parallel processing (PP) memory 204.In general, a parallel processing subsystem includes a number U of PPUs,where U≧1. (Herein, multiple instances of like objects are denoted withreference numbers identifying the object and parenthetical numbersidentifying the instance where needed.) PPUs 202 and parallel processingmemories 204 may be implemented using one or more integrated circuitdevices, such as programmable processors, application specificintegrated circuits (ASICs), or memory devices, or in any othertechnically feasible fashion.

Referring again to FIG. 2A, in some embodiments, some or all of PPUs 202in parallel processing subsystem 112 are graphics processors withrendering pipelines that can be configured to perform various tasksrelated to generating pixel data from graphics data supplied by CPU 102and/or system memory 104 via memory bridge 105 and bus 113, interactingwith local parallel processing memory 204 (which can be used as graphicsmemory including, e.g., a conventional frame buffer) to store and updatepixel data, delivering pixel data to display device 110, and the like.In some embodiments, parallel processing subsystem 112 may include oneor more PPUs 202 that operate as graphics processors and one or moreother PPUs 202 that are used for general-purpose computations. The PPUsmay be identical or different, and each PPU may have its own dedicatedparallel processing memory device(s) or no dedicated parallel processingmemory device(s). One or more PPUs 202 may output data to display device110 or each PPU 202 may output data to one or more display devices 110.

In operation, CPU 102 is the master processor of computer system 100,controlling and coordinating operations of other system components. Inparticular, CPU 102 issues commands that control the operation of PPUs202. In some embodiments, CPU 102 writes a stream of commands for eachPPU 202 to a pushbuffer (not explicitly shown in either FIG. 2A or FIG.2B) that may be located in system memory 104, parallel processing memory204, or another storage location accessible to both CPU 102 and PPU 202.PPU 202 reads the command stream from the pushbuffer and then executescommands asynchronously relative to the operation of CPU 102.

Referring back now to FIG. 2B, each PPU 202 includes an I/O(input/output) unit 205 that communicates with the rest of computersystem 100 via communication path 113, which connects to memory bridge105 (or, in one alternative embodiment, directly to CPU 102). Theconnection of PPU 202 to the rest of computer system 100 may also bevaried. In some embodiments, parallel processing subsystem 112 isimplemented as an add-in card that can be inserted into an expansionslot of computer system 100. In other embodiments, a PPU 202 can beintegrated on a single chip with a bus bridge, such as memory bridge 105or I/O bridge 107. In still other embodiments, some or all elements ofPPU 202 may be integrated on a single chip with CPU 102.

In one embodiment, communication path 113 is a PCI-EXPRESS link, inwhich dedicated lanes are allocated to each PPU 202, as is known in theart. Other communication paths may also be used. An I/O unit 205generates packets (or other signals) for transmission on communicationpath 113 and also receives all incoming packets (or other signals) fromcommunication path 113, directing the incoming packets to appropriatecomponents of PPU 202. For example, commands related to processing tasksmay be directed to a host interface 206, while commands related tomemory operations (e.g., reading from or writing to parallel processingmemory 204) may be directed to a memory crossbar unit 210. Hostinterface 206 reads each pushbuffer and outputs the work specified bythe pushbuffer to a front end 212.

Each PPU 202 advantageously implements a highly parallel processingarchitecture. As shown in detail, PPU 202(0) includes a processingcluster array 230 that includes a number C of general processingclusters (GPCs) 208, where C≧1. Each GPC 208 is capable of executing alarge number (e.g., hundreds or thousands) of threads concurrently,where each thread is an instance of a program. In various applications,different GPCs 208 may be allocated for processing different types ofprograms or for performing different types of computations. For example,in a graphics application, a first set of GPCs 208 may be allocated toperform patch tessellation operations and to produce primitivetopologies for patches, and a second set of GPCs 208 may be allocated toperform tessellation shading to evaluate patch parameters for theprimitive topologies and to determine vertex positions and otherper-vertex attributes. The allocation of GPCs 208 may vary dependent onthe workload arising for each type of program or computation.

GPCs 208 receive processing tasks to be executed via a work distributionunit 200, which receives commands defining processing tasks from frontend unit 212. Processing tasks include indices of data to be processed,e.g., surface (patch) data, primitive data, vertex data, and/or pixeldata, as well as state parameters and commands defining how the data isto be processed (e.g., what program is to be executed). Workdistribution unit 200 may be configured to fetch the indicescorresponding to the tasks, or work distribution unit 200 may receivethe indices from front end 212. Front end 212 ensures that GPCs 208 areconfigured to a valid state before the processing specified by thepushbuffers is initiated.

When PPU 202 is used for graphics processing, for example, theprocessing workload for each patch is divided into approximately equalsized tasks to enable distribution of the tessellation processing tomultiple GPCs 208. A work distribution unit 200 may be configured toproduce tasks at a frequency capable of providing tasks to multiple GPCs208 for processing. By contrast, in conventional systems, processing istypically performed by a single processing engine, while the otherprocessing engines remain idle, waiting for the single processing engineto complete its tasks before beginning their processing tasks. In someembodiments of the present invention, portions of GPCs 208 areconfigured to perform different types of processing. For example a firstportion may be configured to perform vertex shading and topologygeneration, a second portion may be configured to perform tessellationand geometry shading, and a third portion may be configured to performpixel shading in screen space to produce a rendered image. Intermediatedata produced by GPCs 208 may be stored in buffers to allow theintermediate data to be transmitted between GPCs 208 for furtherprocessing.

Memory interface 214 includes a number D of partition units 215 that areeach directly coupled to a portion of parallel processing memory 204,where D≧1. As shown, the number of partition units 215 generally equalsthe number of DRAM 220. In other embodiments, the number of partitionunits 215 may not equal the number of memory devices. Persons skilled inthe art will appreciate that DRAM 220 may be replaced with othersuitable storage devices and can be of generally conventional design. Adetailed description is therefore omitted. Render targets, such as framebuffers or texture maps may be stored across DRAMs 220, allowingpartition units 215 to write portions of each render target in parallelto efficiently use the available bandwidth of parallel processing memory204.

Any one of GPCs 208 may process data to be written to any of the DRAMs220 within parallel processing memory 204. Crossbar unit 210 isconfigured to route the output of each GPC 208 to the input of anypartition unit 215 or to another GPC 208 for further processing. GPCs208 communicate with memory interface 214 through crossbar unit 210 toread from or write to various external memory devices. In oneembodiment, crossbar unit 210 has a connection to memory interface 214to communicate with I/O unit 205, as well as a connection to localparallel processing memory 204, thereby enabling the processing coreswithin the different GPCs 208 to communicate with system memory 104 orother memory that is not local to PPU 202. In the embodiment shown inFIG. 2B, crossbar unit 210 is directly connected with I/O unit 205.Crossbar unit 210 may use virtual channels to separate traffic streamsbetween the GPCs 208 and partition units 215.

Again, GPCs 208 can be programmed to execute processing tasks relatingto a wide variety of applications, including but not limited to, linearand nonlinear data transforms, filtering of video and/or audio data,modeling operations (e.g., applying laws of physics to determineposition, velocity and other attributes of objects), image renderingoperations (e.g., tessellation shader, vertex shader, geometry shader,and/or pixel shader programs), and so on. PPUs 202 may transfer datafrom system memory 104 and/or local parallel processing memories 204into internal (on-chip) memory, process the data, and write result databack to system memory 104 and/or local parallel processing memories 204,where such data can be accessed by other system components, includingCPU 102 or another parallel processing subsystem 112.

A PPU 202 may be provided with any amount of local parallel processingmemory 204, including no local memory, and may use local memory andsystem memory in any combination. For instance, a PPU 202 can be agraphics processor in a unified memory architecture (UMA) embodiment. Insuch embodiments, little or no dedicated graphics (parallel processing)memory would be provided, and PPU 202 would use system memoryexclusively or almost exclusively. In UMA embodiments, a PPU 202 may beintegrated into a bridge chip or processor chip or provided as adiscrete chip with a high-speed link (e.g., PCI-EXPRESS) connecting thePPU 202 to system memory via a bridge chip or other communication means.

As noted above, any number of PPUs 202 can be included in a parallelprocessing subsystem 112. For instance, multiple PPUs 202 can beprovided on a single add-in card, or multiple add-in cards can beconnected to communication path 113, or one or more of PPUs 202 can beintegrated into a bridge chip. PPUs 202 in a multi-PPU system may beidentical to or different from one another. For instance, different PPUs202 might have different numbers of processing cores, different amountsof local parallel processing memory, and so on. Where multiple PPUs 202are present, those PPUs may be operated in parallel to process data at ahigher throughput than is possible with a single PPU 202. Systemsincorporating one or more PPUs 202 may be implemented in a variety ofconfigurations and form factors, including desktop, laptop, or handheldpersonal computers, servers, workstations, game consoles, embeddedsystems, and the like.

Processing Cluster Array Overview

FIG. 3A is a block diagram of a GPC 208 within one of the PPUs 202 ofFIG. 2B, according to one embodiment of the present invention. Each GPC208 may be configured to execute a large number of threads in parallel,where the term “thread” refers to an instance of a particular programexecuting on a particular set of input data. In some embodiments,single-instruction, multiple-data (SIMD) instruction issue techniquesare used to support parallel execution of a large number of threadswithout providing multiple independent instruction units. In otherembodiments, single-instruction, multiple-thread (SIMT) techniques areused to support parallel execution of a large number of generallysynchronized threads, using a common instruction unit configured toissue instructions to a set of processing engines within each one of theGPCs 208. Unlike a SIMD execution regime, where all processing enginestypically execute identical instructions, SIMT execution allowsdifferent threads to more readily follow divergent execution pathsthrough a given thread program. Persons skilled in the art willunderstand that a SIMD processing regime represents a functional subsetof a SIMT processing regime.

Operation of GPC 208 is advantageously controlled via a pipeline manager305 that distributes processing tasks to streaming multiprocessors(SPMs) 310. Pipeline manager 305 may also be configured to control awork distribution crossbar 330 by specifying destinations for processeddata output by SPMs 310.

In one embodiment, each GPC 208 includes a number M of SPMs 310, whereM≧1, each SPM 310 configured to process one or more thread groups. Also,each SPM 310 advantageously includes an identical set of functionalexecution units (e.g., execution units and load-store units—shown asExec units 302 and LSUs 303 in FIG. 3C) that may be pipelined, allowinga new instruction to be issued before a previous instruction hasfinished, as is known in the art. Any combination of functionalexecution units may be provided. In one embodiment, the functional unitssupport a variety of operations including integer and floating pointarithmetic (e.g., addition and multiplication), comparison operations,Boolean operations (AND, OR, XOR), bit-shifting, and computation ofvarious algebraic functions (e.g., planar interpolation, trigonometric,exponential, and logarithmic functions, etc.); and the samefunctional-unit hardware can be leveraged to perform differentoperations.

The series of instructions transmitted to a particular GPC 208constitutes a thread, as previously defined herein, and the collectionof a certain number of concurrently executing threads across theparallel processing engines (not shown) within an SPM 310 is referred toherein as a “warp” or “thread group.” As used herein, a “thread group”refers to a group of threads concurrently executing the same program ondifferent input data, with one thread of the group being assigned to adifferent processing engine within an SPM 310. A thread group mayinclude fewer threads than the number of processing engines within theSPM 310, in which case some processing engines will be idle duringcycles when that thread group is being processed. A thread group mayalso include more threads than the number of processing engines withinthe SPM 310, in which case processing will take place over consecutiveclock cycles. Since each SPM 310 can support up to G thread groupsconcurrently, it follows that up to G*M thread groups can be executingin GPC 208 at any given time.

Additionally, a plurality of related thread groups may be active (indifferent phases of execution) at the same time within an SPM 310. Thiscollection of thread groups is referred to herein as a “cooperativethread array” (“CTA”) or “thread array.” The size of a particular CTA isequal to m*k, where k is the number of concurrently executing threads ina thread group and is typically an integer multiple of the number ofparallel processing engines within the SPM 310, and m is the number ofthread groups simultaneously active within the SPM 310. The size of aCTA is generally determined by the programmer and the amount of hardwareresources, such as memory or registers, available to the CTA.

Each SPM 310 contains an L1 cache (not shown) or uses space in acorresponding L1 cache outside of the SPM 310 that is used to performload and store operations. Each SPM 310 also has access to L2 cacheswithin the partition units 215 that are shared among all GPCs 208 andmay be used to transfer data between threads. Finally, SPMs 310 alsohave access to off-chip “global” memory, which can include, e.g.,parallel processing memory 204 and/or system memory 104. It is to beunderstood that any memory external to PPU 202 may be used as globalmemory. Additionally, an L1.5 cache 335 may be included within the GPC208, configured to receive and hold data fetched from memory via memoryinterface 214 requested by SPM 310, including instructions, uniformdata, and constant data, and provide the requested data to SPM 310.Embodiments having multiple SPMs 310 in GPC 208 beneficially sharecommon instructions and data cached in L1.5 cache 335.

Each GPC 208 may include a memory management unit (MMU) 328 that isconfigured to map virtual addresses into physical addresses. In otherembodiments, MMU(s) 328 may reside within the memory interface 214. TheMMU 328 includes a set of page table entries (PTEs) used to map avirtual address to a physical address of a tile and optionally a cacheline index. The MMU 328 may include address translation lookasidebuffers (TLB) or caches which may reside within multiprocessor SPM 310or the L1 cache or GPC 208. The physical address is processed todistribute surface data access locality to allow efficient requestinterleaving among partition units. The cache line index may be used todetermine whether of not a request for a cache line is a hit or miss.

In graphics and computing applications, a GPC 208 may be configured suchthat each SPM 310 is coupled to a texture unit 315 for performingtexture mapping operations, e.g., determining texture sample positions,reading texture data, and filtering the texture data. Texture data isread from an internal texture L1 cache (not shown) or in someembodiments from the L1 cache within SPM 310 and is fetched from an L2cache, parallel processing memory 204, or system memory 104, as needed.Each SPM 310 outputs processed tasks to work distribution crossbar 330in order to provide the processed task to another GPC 208 for furtherprocessing or to store the processed task in an L2 cache, parallelprocessing memory 204, or system memory 104 via crossbar unit 210. ApreROP (pre-raster operations) 325 is configured to receive data fromSPM 310, direct data to ROP units within partition units 215, andperform optimizations for color blending, organize pixel color data, andperform address translations.

It will be appreciated that the core architecture described herein isillustrative and that variations and modifications are possible. Anynumber of processing units, e.g., SPMs 310 or texture units 315, preROPs325 may be included within a GPC 208. Further, while only one GPC 208 isshown, a PPU 202 may include any number of GPCs 208 that areadvantageously functionally similar to one another so that executionbehavior does not depend on which GPC 208 receives a particularprocessing task. Further, each GPC 208 advantageously operatesindependently of other GPCs 208 using separate and distinct processingunits, L1 caches, and so on.

FIG. 3B is a block diagram of a partition unit 215 within one of thePPUs 202 of FIG. 2B, according to one embodiment of the presentinvention. As shown, partition unit 215 includes a L2 cache 350, a framebuffer (FB) DRAM interface 355, and a raster operations unit (ROP) 360.L2 cache 350 is a read/write cache that is configured to perform loadand store operations received from crossbar unit 210 and ROP 360. Readmisses and urgent writeback requests are output by L2 cache 350 to FBDRAM interface 355 for processing. Dirty updates are also sent to FB 355for opportunistic processing. FB 355 interfaces directly with DRAM 220,outputting read and write requests and receiving data read from DRAM220.

In graphics applications, ROP 360 is a processing unit that performsraster operations, such as stencil, z test, blending, and the like, andoutputs pixel data as processed graphics data for storage in graphicsmemory. In some embodiments of the present invention, ROP 360 isincluded within each GPC 208 instead of partition unit 215, and pixelread and write requests are transmitted over crossbar unit 210 insteadof pixel fragment data.

The processed graphics data may be displayed on display device 110 orrouted for further processing by CPU 102 or by one of the processingentities within parallel processing subsystem 112. Each partition unit215 includes a ROP 360 in order to distribute processing of the rasteroperations. In some embodiments, ROP 360 may be configured to compress zor color data that is written to memory and decompress z or color datathat is read from memory.

Persons skilled in the art will understand that the architecturedescribed in FIGS. 2A, 2B, 3A, and 3B in no way limits the scope of thepresent invention and that the techniques taught herein may beimplemented on any properly configured processing unit, including,without limitation, one or more CPUs, one or more multi-core CPUs, oneor more PPUs 202, one or more GPCs 208, one or more graphics or specialpurpose processing units, or the like, without departing the scope ofthe present invention.

In embodiments of the present invention, it is desirable to use PPU 202or other processor(s) of a computing system to execute general-purposecomputations using thread arrays. Each thread in the thread array isassigned a unique thread identifier (“thread ID”) that is accessible tothe thread during its execution. The thread ID, which can be defined asa one-dimensional or multi-dimensional numerical value controls variousaspects of the thread's processing behavior. For instance, a thread IDmay be used to determine which portion of the input data set a thread isto process and/or to determine which portion of an output data set athread is to produce or write.

A sequence of per-thread instructions may include at least oneinstruction that defines a cooperative behavior between therepresentative thread and one or more other threads of the thread array.For example, the sequence of per-thread instructions might include aninstruction to suspend execution of operations for the representativethread at a particular point in the sequence until such time as one ormore of the other threads reach that particular point, an instructionfor the representative thread to store data in a shared memory to whichone or more of the other threads have access, an instruction for therepresentative thread to atomically read and update data stored in ashared memory to which one or more of the other threads have accessbased on their thread IDs, or the like. The CTA program can also includean instruction to compute an address in the shared memory from whichdata is to be read, with the address being a function of thread ID. Bydefining suitable functions and providing synchronization techniques,data can be written to a given location in shared memory by one threadof a CTA and read from that location by a different thread of the sameCTA in a predictable manner. Consequently, any desired pattern of datasharing among threads can be supported, and any thread in a CTA canshare data with any other thread in the same CTA. The extent, if any, ofdata sharing among threads of a CTA is determined by the CTA program;thus, it is to be understood that in a particular application that usesCTAs, the threads of a CTA might or might not actually share data witheach other, depending on the CTA program, and the terms “CIA” and“thread array” are used synonymously herein.

FIG. 3C is a block diagram of the SPM 310 of FIG. 3A, according to oneembodiment of the present invention. The SPM 310 includes an instructionL1 cache 370 that is configured to receive instructions and constantsfrom memory via L1.5 cache 335. A warp scheduler and instruction unit312 receives instructions and constants from the instruction L1 cache370 and controls local register file 304 and SPM 310 functional unitsaccording to the instructions and constants. The SPM 310 functionalunits include N exec (execution or processing) units 302 and Pload-store units (LSU) 303.

SPM 310 provides on-chip (internal) data storage with different levelsof accessibility. Special registers (not shown) are readable but notwriteable by LSU 303 and are used to store parameters defining each CTAthread's “position.” In one embodiment, special registers include oneregister per CTA thread (or per exec unit 302 within SPM 310) thatstores a thread ID; each thread ID register is accessible only by arespective one of the exec unit 302. Special registers may also includeadditional registers, readable by all CTA threads (or by all LSUs 303)that store a CTA identifier, the CTA dimensions, the dimensions of agrid to which the CTA belongs, and an identifier of a grid to which theCTA belongs. Special registers are written during initialization inresponse to commands received via front end 212 from device driver 103and do not change during CTA execution.

A parameter memory (not shown) stores runtime parameters (constants)that can be read but not written by any CTA thread (or any LSU 303). Inone embodiment, device driver 103 provides parameters to the parametermemory before directing SPM 310 to begin execution of a CTA that usesthese parameters. Any CTA thread within any CTA (or any exec unit 302within SPM 310) can access global memory through a memory interface 214.Portions of global memory may be stored in the L1 cache 320.

Local register file 304 is used by each CTA thread as scratch space;each register is allocated for the exclusive use of one thread, and datain any of local register file 304 is accessible only to the CTA threadto which it is allocated. Local register file 304 can be implemented asa register file that is physically or logically divided into P lanes,each having some number of entries (where each entry might store, e.g.,a 32-bit word). One lane is assigned to each of the N exec units 302 andP load-store units LSU 303, and corresponding entries in different lanescan be populated with data for different threads executing the sameprogram to facilitate SIMD execution. Different portions of the lanescan be allocated to different ones of the G concurrent thread groups, sothat a given entry in the local register file 304 is accessible only toa particular thread. In one embodiment, certain entries within the localregister file 304 are reserved for storing thread identifiers,implementing one of the special registers.

Shared memory 306 is accessible to all CTA threads (within a singleCTA); any location in shared memory 306 is accessible to any CTA threadwithin the same CTA (or to any processing engine within SPM 310). Sharedmemory 306 can be implemented as a shared register file or sharedon-chip cache memory with an interconnect that allows any processingengine to read from or write to any location in the shared memory. Inother embodiments, shared state space might map onto a per-CTA region ofoff-chip memory, and be cached in L1 cache 320. The parameter memory canbe implemented as a designated section within the same shared registerfile or shared cache memory that implements shared memory 306, or as aseparate shared register file or on-chip cache memory to which the LSUs303 have read-only access. In one embodiment, the area that implementsthe parameter memory is also used to store the CTA ID and grid ID, aswell as CTA and grid dimensions, implementing portions of the specialregisters. Each LSU 303 in SPM 310 is coupled to a unified addressmapping unit 352 that converts an address provided for load and storeinstructions that are specified in a unified memory space into anaddress in each distinct memory space. Consequently, an instruction maybe used to access any of the local, shared, or global memory spaces byspecifying an address in the unified memory space.

The L1 Cache 320 in each SPM 310 can be used to cache private per-threadlocal data and also per-application global data. In some embodiments,the per-CTA shared data may be cached in the L1 cache 320. The LSUs 303are coupled to a uniform L1 cache 375, the shared memory 306, and the L1cache 320 via a memory and cache interconnect 380. The uniform L1 cache375 is configured to receive read-only data and constants from memoryvia the L1.5 Cache 335.

Decomposing Cubic Bèzier Segments

A path consists of a sequence of connected path segment commands forline segments, Bèzier segments, and partial elliptical arcs. CubicBèzier segments pose a particular challenge when rendering thesesegments into the stencil buffer to determine what framebuffer samplelocations are within the filled region of the respective path. If notdone carefully, multiple classes of cubic Bèzier segments can contributeincorrect winding number offsets to the net winding number for aparticular framebuffer sample location. An incorrect winding numberdetermination immediately leads to an incorrect determination of therasterized filled region of said path. Decomposing each arbitrary cubicBèzier in a path into one or more simple cubic Bèzier segments producesa geometry set that is suitable for rendering filled paths containingcubic Bèzier segments. Such decomposition is beneficial because itresults in a robust determination of the filled region of a renderedpath without tessellating the path. The path is divided into cubicBèzier path segments that are each classified and further divided intosimple cubic Bèzier path segments. Care must be taken to preserve theproper vertex winding order of each simple Bèzier cubic segment, splitthe original cubic Bèzier at the proper positions, and linearlyinterpolate texture coordinates according to the technique described byLoop and Blinn for use with a discard shader. The simple cubic Bèzierpath segments are then rasterized using a discard shader program togenerate a stencil buffer indicating pixels that are inside of the path.In contrast, the discard shader technique described by Loop and Blinnfills the inside of the path by rendering the tessellated Bèzier curvesegments using the discard shader to write directly to the color buffer.

Bèzier curves are defined by their control points. In the 2D content ofpath rendering, each control point is a 2D position. Curved pathsegments for a path may be generated by path commands for quadraticBèzier curves, cubic Bèzier curves, and partial elliptical arcs.

A quadratic Bèzier curve is specified by 3 control points and a cubicBèzier curve is specified by 4 control points. The QUADRATICTO commanduses the terminal position of the prior command as its initial controlpoint (x0,y0) and then 4 associated coordinates form the two new (x1,y1)and (x2,y2) control points. The quadratic Bèzier curve starts at (x0,y0)heading towards (x1,y1) and ends at (x2,y2) as if coming from (x1,y1).Despite (x1,y1) providing the initial tangent direction when startingfrom (x0,y0) and terminating at (x2,y2), the resulting curve does notpass through (x1,y1); for this reason, (x1,y1) is known as anextrapolating control point while (x0,y0) and (x2,y2) are known asinterpolating control points. Quadratic Bèzier curves may be filledwithout tessellation manner, because non-degenerate quadratic Bèziercurves have no points of self-intersection and the segment curve doesnot intersect the line formed by the initial and terminal controlpoints.

The CUBIC _(T) O command is similar to the QUADRATICTO command butgenerates a cubic Bèzier curve. Such a curve is specified by 4 controlpoints. The CUBICTO command uses the terminal position of the priorcommand as its initial control point (x0,y0) and then 6 associatedcoordinates form the 3 new (x1,y1), (x2,y2), and (x3,y3) control points.The cubic Bèzier curve starts at (x0,y0) heading towards (x1,y1) andends at (x3,y3) as if coming from (x2,y2). While a quadratic Bèziercurve has a single extrapolating control point, cubic Bèzier curves havetwo extrapolating control points, (x1,y1) and (x2,y2). A cubic Bèziercurve has the freedom, unlike a quadratic Bèzier curve, to specifyarbitrary initial and terminal tangent directions for its end-points.This control makes cubic Bèzier curves popular with artists. Thisadditional control comes from the curve being described by a third-orderpolynomial equation instead of a second-order equation in the case of aquadratic Bèzier curve (and first-order in the case of line segments).This additional polynomial degree provides the requisite freedom for acubic Bèzier segment to non-trivially self-intersect itself or cross theline formed by the segment's initial and terminal control points. Theseconditions result in reversals of the local sense of “inside” and“outside” the path. In order for a tessellation-free path fillingapproach based on stencil counting of rasterized polygons to be robustwhen a discard shader is used to write a stencil buffer, such situationsmust be avoided. The present invention describes such an approach thatpreserves the efficiency of evaluating the implicit representation ofcubic Bèzier segments described by Loop and Blinn is used by a discardshader to write the stencil buffer.

FIG. 5A illustrates a simple cubic Bèzier path segment 500 of a path,according to one embodiment of the invention. The simple cubic Bèzierpath segment 500 may be one of many segments that define a closed pathloop. The simple cubic Bèzier path segment 500 starts at a firstinterpolating control point, segment base vertex 502 and ends at asecond interpolating control point, segment base vertex 506. The simplecubic Bèzier path segment 500 has two extrapolating control points,control point 503 and control point 504. Parameters for the simple cubicBèzier path segment 500 are generated by linearly interpolatingparameters that specify the cubic Bèzier path segment from which thesimple cubic Bèzier path segment 500 originated. A polygon, convex hullgeometry 510 is constructed for the simple cubic Bèzier path segment 500such that each vertex of the convex hull geometry 510 is coincident witha control point of the simple cubic Bèzier path segment 500. The 4-sidedconvex hull geometry 510 is defined by the segment base vertex 502,control point 503, control point 504, and segment base vertex 506 andhas a winding order that is clockwise because the convex hull geometry510 is front-facing.

An anchor vertex 501 is determined for the closed path loop (potentiallya sub-path of the complete path containing multiple such path loops)containing the simple cubic Bèzier path segment 500. For clarity ofillustration, FIG. 5A shows just a single path segment and not theclosed loop within which the segments is a part. This loop would consistof one or more additional path segments looping from segment base vertex506 and eventually connecting back to segment base vertex 502. Anchorgeometry 505 is a triangle defined by the anchor vertex 501, segmentbase vertex 502, and segment base vertex 506 has a winding order that isconsistent with the path segment 500. The winding order of the anchorgeometry 505 is clockwise because the anchor geometry 505 isfront-facing.

The anchor vertex 501 may be located anywhere within the 2D planecontaining the path containing path segment 500. What matters is thatevery path segment residing on the path look containing path segment 500share the same anchor vertex. This shared anchor vertex for all theloop's path segments ensures the winding number counting performedthrough a rasterization process has a consistent neutral position fromwhich to rasterize and count. A good choice for the anchor vertexlocation is any segment base vertex (such as 502 or 506) because thatforces at least one anchor geometry triangle to be zero area such thatit need not be rasterized. Additionally choosing an anchor vertex nearthe centroid of the closed path's filled region tends to minimize theoverall rasterization processing.

A set of stencil values in a stencil buffer may be generated thatindicates the pixels, or more generally framebuffer sample locations,that are within the path segment 500 by incrementing each stencil buffervalue corresponding to pixels that are within the front-facing hullgeometry 510 and incrementing each stencil buffer value corresponding topixels that are within the front-facing anchor geometry 505. Likewise,if the hull geometry or anchor geometry was back-facing, therasterization process would decrement each stencil buffer valuecorresponding to pixels within said geometry. When rendering the hulland anchor geometry, the vertices belonging to this geometry are subjectto an arbitrary projective transformation so the sense of front- orback-facing in object space may be the opposite sense after vertextransformation. In one embodiment, the ROP 360 (alternatively rasteroperations unit 465) performs the increments and decrements of stencilwhile the rasterizer 455 rasterizes the geometry.

In one embodiment, batches of hull geometry and anchor geometry aredrawn together that mix front- and back-facing polygons such thattwo-sided stencil testing can increment and decrement the stencil basedon each polygon's determined facingness. The color and depth writes aredisabled during generation of the stencil buffer. Once the stencilbuffer is complete, writes to the color buffer are enabled and thepixels that are inside of the path may be filled by using the stencilbuffer to write the color buffer when a conservative bounding geometrythat encloses a closed path including the path segment 500 is rendered.During this second rendering pass to cover the path, the stencil valuescan be restored to their value prior to writing of the stencil buffer inthe first rendering pass.

In order to fill only the portion of the hull geometry 510 that isinside of the path segment 500 (indicated by the fill pattern), valuesof the stencil buffer corresponding to the pixels that are located inthe portion of the hull geometry 510 that is between the path segment500 and the edges of the hull geometry 510 defined by segment basevertex 502, control point 503, control point 504, and the segment basevertex 506 should not be incremented or decremented. In other words,pixels within the hull geometry 510 and outside of the path segment 500should be disabled. The parameters defining the path segment 500 may belinearly interpolated as texture map coordinates for each pixel withinthe hull geometry 510. The interpolated texture coordinates for eachpixel may then be used to determine whether the pixel is inside the pathsegment 500. The technique of calculating texture coordinates todetermine whether a pixel is inside of a path segment is described byCharles Loop and Jim Blinn (in Resolution Independent Curve Renderingusing Programmable Graphics Hardware, ACM Transactions on Graphics,Volume 24, Issue 3, July 2005) and is summarized here.

Simple cubic and quadratic Bèzier segments may be processed by afragment shader program to determine if each fragment or sample isinside or outside of the path segment 500. Rendering quadratic Bèzierpath segments in this manner is straightforward. The shader programevaluates the following boolean expression depending on two texturecoordinates (s,t):

Q(s,t)=s ² >t

If Q(s,t) is true, the sample should be discarded; otherwise the sampleis within the quadratic Bèzier path segment and should be rendered.

Rendering cubic Bèzier path segments is more complex. The fragmentshader program evaluates the following boolean expression depending onthree texture coordinates (s,t,r):

C(s,t,r)=s ³ >tr

If C(s,t,r) is true, the sample should be discarded; otherwise thesample is within the cubic Bèzier path segment 500 and should berendered. Computing the texture coordinates needed for the cubic Bèzierpath segment 500 involves classifying the topology of the path(serpentine, cusp, loop, or a degenerate quadratic, line, or point).

The technique described by Loop and Blinn assumes that the interior ofpaths has been tessellated so that Bèzier path segments lie only on theboundary of the path. As previously explained, tessellation isburdensome in terms of both performance and the amount of data that isgenerated. In order to avoid tessellation of the interior of the path, anew technique is used that characterizes the topology of the cubicBèzier path segments and divides the cubic Bèzier path segments intosimple cubic Bèzier path segments based on the characterization of eachcubic Bèzier path segment. The efficient discard shader techniquedeveloped by Loop and Blinn is used to remove pixels that are outside ofthe simple cubic Bèzier path segments. In contrast with the newtechnique and the discard shader technique, Rueda et al. describe atechnique that relies on a less efficient cubic Bèzier normalizationrequiring many more arithmetic operations for each cubic Bèzier curvethat is tested against a pixel.

Texture coordinates are associated with the vertices of the anchortriangles and the texture coordinates are interpolated and used by adiscard shader program to determine the pixels of the convex hullgeometry 510 that are inside of the path segment 500. The discard shaderprogram first discards any pixels that are outside of the path segment500 based on the interpolated texture coordinates and then increments ordecrements the stencil buffer values corresponding to the survivingpixels based on the winding order of the convex hull geometry 510. Inone embodiment, stencil values are incremented for front-facing(clockwise winding) primitives and decremented for back-facing(counter-clockwise winding) primitives. In another embodiment, stencilvalues are decremented for front-facing (clockwise winding) primitivesand incremented for back-facing (counter-clockwise winding) primitives.In yet another embodiment, the convention for front-facing iscounter-clockwise while back-facing is clockwise. Writes to the colorand depth buffer are disabled during execution of the discard shader.

A stencil shader is executed to render the anchor geometry 505 and,based on the winding order of the anchor geometry 505, values in thestencil buffer are incremented or decremented for pixels that are withinthe anchor geometry 505. The winding order of 505 is such that thedirection of winding from 502 to 506 is the opposite direction as usedfor the convex hull geometry 510. In the FIG. 5A example, the convexhull geometry 510 winds clockwise from vertices 503 to 504 to 506 to502. So the winding for anchor geometry 505 must wind 501 to 502 to 506(opposite of 506 to 502). Writes to the color and depth buffer aredisabled during execution of the stencil shader. The stencil shader maybe executed before or after the discard shader.

After the stencil buffer is updated for all of the path segments of apath, the resulting stencil buffer indicates the pixels that are insideof the closed path that includes the path segment 500. Writes to thecolor buffer are enabled and a fill shader program is then executed tofill the inside of the closed path using the generated stencil bufferwhile rendering a bounding geometry. The stencil buffer may be clearedfor each pixel as a fill color is written to the color buffer for therespective pixel. Clearing the stencil value of each pixel isstraightforward to accomplish with standard stencil operations such asZero or Replace. The bounding geometry may be a set of polygons,including a polygon defined by all of the vertices of both the convexhull geometry 510 and anchor geometry 505. Alternatively, the boundinggeometry may be a single polygon that encloses the entire closed path tobe filled. The bounding geometry should conservatively enclose the pathto be filled.

FIG. 5B illustrates another path segment 520 that is also a simpleBèzier cubic path segment, according to one embodiment of the invention.The simple cubic Bèzier path segment 520 starts at a first interpolatingcontrol point, segment base vertex 522 and ends at a secondinterpolating control point, segment base vertex 526. The simple cubicBèzier path segment 520 has two extrapolating control points, controlpoint 523 and control point 524. Note that the control point 523 isinside of the path segment 520.

Parameters for the simple cubic Bèzier path segment 520 are generated bylinearly interpolating parameters that specify the cubic Bèzier pathsegment from which the simple cubic Bèzier path segment 520 originated.A polygon, convex hull geometry 530 is constructed for the simple cubicBèzier path segment 520 such that each vertex of the convex hullgeometry 530 is coincident with a control point of the simple cubicBèzier path segment 520. The 3-sided convex hull geometry 530 is definedby the segment base vertex 522, control point 524, and segment basevertex 526 and is front-facing. An anchor vertex 521 is determined forthe closed path loop containing the simple cubic Bèzier path segment 520and an anchor geometry 525 (triangle) is defined by the anchor vertex521, the segment base vertex 526, and the segment base vertex 522. Theanchor geometry 525 is also front-facing.

Texture coordinates are associated with the vertices of the anchortriangles and the texture coordinates are interpolated and used by thediscard shader program to determine the pixels of the convex hullgeometry 530 that are inside of the path segment 520. The discard shaderprogram first discards any pixels that are outside of the path segment520 based on the interpolated texture coordinates and then updates thestencil buffer values corresponding to the surviving pixels based on thewinding order of the convex hull geometry 530. The anchor geometry 525is also rasterized though without requiring texture coordinates andwithout a discard shader so that, based on the winding order of theanchor geometry 525, values in the stencil buffer are updated for pixelsthat are within the anchor geometry 525. Writes to the color and depthbuffer are disabled during execution of the discard shader and thestencil shader. In one embodiment, anchor polygons rasterize at a fasterrate than shaded polygons, often double the peak rate for shadedpolygons, because no attributes need to be interpolated, no shaderexecution need be initiated, and no color writes are necessary. Thisfaster rate of stencil-only, shader-free rasterization for anchorpolygons is advantageous because anchor polygons tend to perform morestencil updates overall compared to the hull geometry that is processedby discard shaders.

After the stencil buffer is updated for all of the path segments of apath, the resulting stencil buffer indicates the pixels that are insideof the closed path that includes the path segment 520. A fill shaderprogram is then executed by rasterizing one or more polygonsconservatively covering the path to fill the inside of the closed pathusing the generated stencil buffer. During this rasterization, the colorbuffer is updated for pixels indicated by the stencil buffer to bewithin the fill of the path; additionally stencil operations can restorethe stencil buffer to its state prior to rasterizing the path's fillinto the stencil buffer.

FIG. 5C illustrates another path segment 540 that is also a simpleBèzier cubic path segment, according to one embodiment of the invention.The simple cubic Bèzier path segment 540 starts at a first interpolatingcontrol point, segment base vertex 542 and ends at a secondinterpolating control point, segment base vertex 546. The simple cubicBèzier path segment 540 has two extrapolating control points, controlpoint 543 and control point 544.

Parameters for the simple cubic Bèzier path segment 540 are generated bylinearly interpolating parameters that specify the cubic Bèzier pathsegment from which the simple cubic Bèzier path segment 540 originated.A polygon, hull geometry 550 is constructed for the simple cubic Bèzierpath segment 540 such that each vertex of the hull geometry 550 iscoincident with a control point of the simple cubic Bèzier path segment540. The 4-sided hull geometry 550 is defined by the segment base vertex542, control point 543, control point 544, and segment base vertex 546.

An anchor vertex 541 is determined for the closed path loop containingthe simple cubic Bèzier path segment 540 and anchor geometry 545 withwinding order consistent with the path segment 540 is defined by theanchor vertex 541, the segment base vertex 542, and the segment basevertex 546. The winding order of the convex hull geometry 550 iscounter-clockwise and the winding order of the anchor geometry 545 isclockwise. Therefore, the stencil buffer is incremented by thefront-facing anchor geometry 545 and decremented by the back-facing hullgeometry 550 for a net change of zero. However only the top portion ofhull geometry 550 above path segment 540 actually decrements the stencilbuffer because the region of the hull geometry 550 below the pathsegment 540 is discarded by the stencil discard shared in this case.Therefore, the pixels within the anchor geometry 545 that are also belowpath segment 550 are incremented (and not decremented) in the stencilbuffer.

Texture coordinates are associated with the vertices of the hullgeometry 550 and the texture coordinates are interpolated and used bythe discard shader program to determine the pixels of the convex hullgeometry 550 that are inside of the path segment 540.

In more detail, the discard shader program then causes the stencilbuffer to decrement for the surviving pixels based on the back-facingwinding order of the convex hull geometry 550. Stencil-only renderingwithout a discard shader is then used to render the anchor geometry 545and, based on the front-facing winding order of the anchor geometry 545,causes the stencil buffer to increment for pixels that are within theanchor geometry 545. The relative effect on the stencil buffer indicatesthat pixels bounded by the path segment 540 and segments having a commonendpoint at the anchor vertex 541 and respective endpoints at thesegment base vertex 542 and the segment base vertex 546 are allincremented by one. Once combined with all the path segments in thepath, the net result is to displace the stencil buffer from its originalvalue by the winding number of each pixel with respect to the completepath.

FIG. 5D illustrates the simple Bèzier cubic path segment 540 and asimple Bèzier cubic path segment 560 that form a closed path, accordingto one embodiment of the invention. The simple cubic Bèzier path segment560 starts at the segment base vertex 546 and ends at the segment basevertex 542. The simple cubic Bèzier path segment 560 has twoextrapolating control points, control point 563 and control point 564.The convex hull geometry 570 is a quadrilateral windingcounter-clockwise and defined by the segment base vertex 546, thecontrol point 564, the control point 563, and the segment base vertex542. The convex hull geometry 550 is also a quadrilateral windingcounter-clockwise and defined by the segment base vertex 542, thecontrol point 543, the control points 544, and the segment based vertex546.

Texture coordinates computed using the technique described by Loop andBlinn are associated with the vertices of the convex hull geometries 550and 570 and the texture coordinates are interpolated and used by thediscard shader program to determine the pixels of the hull geometries550 and 570 that are inside of the closed path including the pathsegment 560 and the path segment 540. The discard shader programdiscards the pixels between the path segment 540 and the edges of thehull geometry 550 starting at the segment base vertex 546, passingthrough the control point 544 and 543, and ending at the segment basevertex 542. The discard shader program then decrements the stencilbuffer for the surviving pixels within the hull geometry 550 and 570based on the similarly counter-clockwise winding order of the respectivehull geometry 550 or 570. Stencil values corresponding to the survivingpixels that are inside of the path formed by the path segments 540 and560 are decremented by the discard shader program. Importantly, thedecrements, as well as any increments, perform modulo or wrappingarithmetic (rather than saturating arithmetic). This is crucial giventhe limited integer precision (typically 8 bits) of the stencil buffer.In this example, this means if the stencil buffer was initially clearedto zero, the result of these decrements to an 8-bit stencil buffer wouldbe the value 255 resulting from modulo-256 arithmetic.

The treatment so far has ignored the anchor geometry in FIG. 5D.Stencil-only rasterization without discarding is then used to render theanchor geometry 545 and, based on the winding order of the anchorgeometry 545, increments or decrements the stencil buffer for pixelsthat are within the anchor geometry 545. The winding order of the anchorgeometry 545 for the path segment 540 is clockwise. The anchor geometryfor the path segment 560 is coincident with the anchor geometry 545, buthas a counter-clockwise winding order. Therefore, values of the stencilbuffer corresponding to pixels in the anchor geometry 545 areincremented and decremented, producing a net stencil change of zero. Inone embodiment, if identical anchor geometry except for opposite windingorder is detected, rasterization of this geometry can be skipped. Due tothe freedom to position the anchor vertex arbitrarily, anotherembodiment could position anchor vertex 541 coincident with eithersegment based vertex 542 or 546 resulting in both instances anchorgeometry 545 having zero area. An embodiment could eliminaterasterization of any such zero area geometry.

After the hull geometries 550 and 570 and both of the anchor geometries545 are rendered to generate the stencil buffer, the stencil buffer willindicate only the pixels that are inside of the path defined by the pathsegments 540 and 560. The generated stencil buffer may then be used tofill the pixels that are inside of the path segment 540, e.g., pixelsbetween the path segment 540 and the segment bounded by the segment basevertex 542 and the segment base vertex 546. A bounding geometry that isa quadrilateral defined by all of the vertices of the path defined bythe path segments 540 and 560, e.g., the segment base vertices 542 and546 and control points 543, 544, 563, and 564, may be rendered to writethe color buffer based on the stencil buffer. The bounding geometryshould conservatively enclose the path to be filled. Rasterization ofthe bounding geometry can test the stencil buffer. Assuming the stencilbuffer was initially cleared to zero, the stencil test can discardupdates to any pixels with a corresponding stencil value of zero, butotherwise update non-zero pixels. In the case of FIG. 5D, the regionbounded by path segments 540 and 560 has a resulting stencil value of255 so this region will be updated. Along with updating the colorbuffer, this covering rasterization can zero the non-zero stencil valuesso subsequent paths can be rendered in a similar manner.

FIG. 6A illustrates a Bèzier cubic path segment 600 that isself-intersecting to form a loop with one root, according to oneembodiment of the invention. The cubic Bèzier path segment 600 starts ata first interpolating control point, segment base vertex 602 and ends ata second interpolating control point, segment base vertex 606. Both ofthe interpolating control points lie on a path base line 607. The cubicBèzier path segment 600 has two extrapolating control points, controlpoint 603 and control point 604 and an anchor vertex 601 is positionedoutside of the path segment 600. For reasons that will be made clear, adashed line emanating from segment based vertex 606 shows how the cubicBèzier curve would continue outside the conventional [0,1] parameterrange of a cubic Bèzier segment. The simple process explained so far forFIGS. 5A, 5B, 5C, and 5D is insufficient to handle the situation in FIG.6A for reasons that are not immediately obvious. The implication is thatthe conventional techniques that are limited to filling quadratic Bèziercurves will not extend in a straightforward way to the situation in FIG.6A as well as additional cases to be discussed. The present inventionprovides a robust way to handle these problem situations while stillmaking use of the efficient-to-evaluate Loop and Blinn cubic curvetexture coordinates. A corresponding discard shader is used to generatea stencil buffer.

FIG. 6B illustrates the anchor geometry for the simple cubic Bèzier pathsegments originating from the self-intersecting cubic Bèzier pathsegment 600, according to one embodiment of the invention. A single rootpoint 615 is located at the position where the path segment 600intersects the continuation of the cubic Bèzier curve. The path segment600 has a single intersection root within the [0,1] parametric intervalsince the endpoints of the parametric interval correspond to the segmentbase vertex 602 and the segment base vertex 606, and the single rootpoint 615 is approximately located at 0.4 in parametric space. If thepath segment 600 continued past the segment base vertex 606, the pathsegment 600's cubic curve would also self-intersect at approximately 1.2in parametric space. However, 1.2 is outside of the parametric intervalof [0,1] so there is only a single intersection on the path segment 600.A cubic Bèzier path segment with a loop topology and a single root pointis divided into two simple cubic Bèzier path segments prior to renderingthe path.

A first simple cubic Bèzier path segment is created using the well-knownDe Casteljau's algorithm for Bèzier curve splitting by starting at thesegment base vertex 602 and ending at the single root point 615. Thefirst simple cubic Bèzier path segment has two extrapolating controlpoints, new control point 612 and new control point 613. Convex hullgeometry for the first simple cubic Bèzier path segment is defined bythe segment base vertex 602, new control point 612, new control point613, and the single root point 615; this hull winds counter-clockwise.Anchor geometry for the first simple cubic Bèzier path segment isdefined by the anchor vertex 601, the segment base vertex 602, and thesingle root point 615; this hull geometry winds counter-clockwise. Thewinding of the anchor geometry is the same as the convex hull geometryfor the first simple cubic Bèzier path segment.

Again using De Casteljau's algorithm, a second simple cubic Bèzier pathsegment is created starting at the single root point 615 and ending atthe segment base vertex 606. The second simple cubic Bèzier path segmentalso has two extrapolating control points, new control point 614 and newcontrol point 616. Counter-clockwise winding convex hull geometry forthe second simple cubic Bèzier path segment is defined by the singleroot point 615, new control point 614, new control point 616, and thesegment base vertex 606. Anchor geometry for the second cubic Bèzierpath segment is defined by the anchor vertex 601, the single root point615, and the segment base vertex 606. The winding of the anchor geometryis counter-clockwise and the same as the convex hull geometry for thesecond simple cubic Bèzier path segment.

After this splitting process, the rationale for splitting can beidentified. Unlike the single path segment 600 in FIG. 6A where thecurve intersects the path base line 607, such crossings are eliminatedin each of the two split path segments on either side of single rootpoint 615 in FIG. 6B. The first path segment does not intersect its pathbase line spanning 602 and 615, and the second path segment does notintersect its path base line spanning 615 and 606. The elimination ofpath segments crossing their base line is crucial for correct netwinding when the complete path is rendered; otherwise an obviouslyincorrect path determination results.

The convex hull geometries are rendered using the discard shader programand the stencil buffer values are updated for the surviving pixels. Thetexture coordinates for the convex hull vertices 612, 613, 614, and 616are efficiently computed by linearly interpolating the Loop and Blinntexture coordinates generated from the original path segment 600'scontrol points. The first and second anchor geometries are processed bythe stencil shader and the stencil values are updated based on thewinding orders. The resulting stencil buffer when combined with all theother path segments of the complete path indicates the pixels that areinside of the complete filled path. A bounding geometry for the entirepath containing path segment 600 may be rendered to write the colorbuffer based on the stencil buffer, filling a closed path that includesthe path segment 600.

FIG. 6C illustrates a Bèzier cubic path segment 650 that isself-intersecting to form a loop with two roots with the parametricinterval [0,1], according to one embodiment of the invention. The cubicBèzier path segment 650 starts at a first interpolating control point,segment base vertex 652 and ends at a second interpolating controlpoint, segment base vertex 655. The cubic Bèzier path segment 650 isdefined by two interpolating control points, and control point 653 and654. An anchor vertex 651 is positioned outside of the path segment 650.Path segment 650 requires splitting because the loop formed by pathsegment 650 needs to be incremented consistently with the non-loopportion of the path segment.

FIG. 6D illustrates the anchor geometry for the simple cubic Bèzier pathsegments originating from the self-intersecting cubic Bèzier pathsegment 650, according to one embodiment of the invention. A double rootpoint 665 is located at the position where the path segment 650intersects itself. The path segment 650 has a double root between the[0,1] parametric interval since there are two points on the path segment650 between the endpoints of the parametric interval that correspond tothe segment base vertex 652 and the segment base vertex 656. A cubicBèzier path segment with a loop topology and a double root point isdivided into three simple cubic Bèzier path segments prior to renderingthe path.

A first simple cubic Bèzier path segment is created starting at thesegment base vertex 652 and ending at the double root point 665. Thefirst simple cubic Bèzier path segment has two extrapolating controlpoints, new control point 667 and new control point 666. Convex hullgeometry winding counter-clockwise for the first simple cubic Bèzierpath segment is defined by the segment base vertex 652, new controlpoint 667, new control point 666, and the double root point 665. Anchorgeometry winding clockwise for the first simple cubic Bèzier pathsegment is defined by the anchor vertex 651, the segment base vertex652, and the double root point 665.

A second simple cubic Bèzier path segment is created starting at thedouble root point 665 and ending at the double root point 665. Thesecond simple cubic Bèzier path segment also has two extrapolatingcontrol points, new control point 663 and new control point 664. Convexhull geometry winding clock-wise for the second simple cubic Bèzier pathsegment is defined by the double root point 665, new control point 663,new control point 664, and the double root point 665. Anchor geometryfor the second cubic Bèzier path segment is degenerate having zero areaso need not be rasterized.

A third simple cubic Bèzier path segment is created starting at thedouble root point 665 and ending at the segment base vertex 655. Thethird simple cubic Bèzier path segment also has two extrapolatingcontrol points, new control point 676 and new control point 677. Convexhull geometry winding counter-clockwise for the third simple cubicBèzier path segment is defined by the segment base vertex 655, newcontrol point 677, new control point 676, and the double root point 665.Anchor geometry winding clockwise for the third cubic Bèzier pathsegment is defined by the anchor vertex 651, double root point 665, andthe segment base vertex 655.

The hull geometries are rendered using the discard shader program todiscard pixels and update the stencil buffer and the first and secondanchor geometries are rendered without discarding to update the stencilbuffer. As in the single root case, the texture coordinates for theconvex hull vertices 667, 666, 663, 664, 676, and 677 are efficientlycomputed by linearly interpolating texture coordinates generated fromthe original path segment 650's control points. The resulting stencilbuffer after all the other path segments in the path containing pathsegment 650 are rendered indicates the pixels that are inside thecomplete path. The stencil buffer is then used to fill a closed paththat includes the path segment 650.

FIG. 7A illustrates a cubic Bèzier path segment 700 that intersects abase line to form a serpentine topology, according to one embodiment ofthe invention. The cubic Bèzier path segment 700 starts at a firstinterpolating control point, segment base vertex 702 and ends at asecond interpolating control point, segment base vertex 705. The cubicBèzier path segment 700 is defined by two interpolating control points,control point 703 and 704. An anchor vertex 701 is positioned inside ofa closed path that includes the path segment 700. The cubic Bèzier pathsegment 700 intersects the path base line 707 between the segment basevertex 702 and the segment base vertex 705 meaning that a region abovethe path base line 707 and below path segment 700 should be stencilincremented and the region below the path base line and above pathsegment 700 should be stencil decremented though this region will alsobe incremented due to an increment from the anchor geometry windingclockwise. Accomplishing this requires splitting the serpentine pathsegment.

FIG. 7B illustrates simple cubic Bèzier path segments originating fromthe cubic Bèzier path segment 700 that intersects a base line to form aserpentine topology, according to one embodiment of the invention. Anintersection point 720 is located at the position where the path segment700 intersects the path base line 707. A cubic Bèzier path segment witha serpentine topology is divided into two simple cubic Bèzier pathsegments prior to rendering the path.

A first simple cubic Bèzier path segment is created starting at thesegment base vertex 702 and ending at the intersection point 720. Thefirst simple cubic Bèzier path segment has two extrapolating controlpoints, new control point 713 and new control point 714. Convex hullgeometry winding clockwise for the first simple cubic Bèzier pathsegment is defined by the segment base vertex 702, the new control point713, and the intersection point 720. Anchor geometry winding clockwisefor the first simple cubic Bèzier path segment is defined by the anchorvertex 701, the segment base vertex 702, and the intersection point 720.The winding of the anchor geometry is the same as the convex hullgeometry for the first simple cubic Bèzier path segment.

A second simple cubic Bèzier path segment is created starting at theintersection point 720 and ending at the segment base vertex 705. Thesecond simple cubic Bèzier path segment has two extrapolating controlpoints, new control point 717 and new control point 716.Counter-clockwise winding convex hull geometry for the second simplecubic Bèzier path segment is defined by the segment base vertex 705, theintersection point 720, and the new control point 717. Clockwise windinganchor geometry for the second simple cubic Bèzier path segment isdefined by the anchor vertex 701, the intersection point 720, and thesegment base vertex 705. The winding of the anchor geometry is thereverse of the convex hull geometry for the second simple cubic Bèzierpath segment.

The hull geometries are rendered using the discard shader program todiscard pixels and update the stencil buffer and the first and secondanchor geometries are rendered without discarding to update the stencilbuffer. As in the prior loop cases, the texture coordinates for theconvex hull vertices 713 and 717 are efficiently computed by linearlyinterpolating the texture coordinates generated from the original pathsegment 650's control points. The resulting stencil buffer incrementsthe pixels that are inside of the first cubic Bèzier path segment anddecrements the stencils inside the second simple cubic Bèzier pathsegment. The stencil buffer is then used to fill the complete closedpath that includes the path segment 700. The pixels between the portionof the path segment 700 within the first convex hull geometry will beincremented and the portion of the path segment 700 within the secondconvex hull geometry will decremented but canceled by the increment fromthe anchor geometry.

A cubic Bèzier path segment may also form a cusp topology that isdetected when the cubic Bèzier discriminate is exactly zero. A cubicBèzier path segment that forms a cusp topology may be divided intosimple cubic Bèzier path segment in the same manner as a serpentinetopology. There are also degenerate fill cases for which an area shouldbe discarded and not filled. For Example points should not be filed.Line segments should be handled as a line segment or using a genericdegenerate (s,t) texture coordinate assignment. Quadratic Bèziersegments should be handled directly as quadratic Bèzier segments orusing a generic degenerate (s,t,r) texture coordinate assignment.

For numeric precision reasons, cubic Bèzier segments that aremasquerading as quadratic Bèzier segments, or that may be represented asa quadratic Bèzier segment, should be demoted and handled as a quadraticBèzier segment. A cusp at infinity should be processed using a specialdegenerate (s,t,r) texture coordinate assignment. A person skilled inthe art will recognize that this discussion exhaustively, robustly, andefficiently handles all the cases necessary to decompose arbitrary cubicBèzier segments into simple cubic Bèzier segments such that whenrendered as described with the complete set of path segments, thepresent invention can determine via a stencil buffer the pixels belongto the filled region of an arbitrary path consisting of cubic andquadratic Bèzier curves and other path segment types such as partialelliptical arcs and line segments. This process is free fromtessellation of the path.

FIG. 8A is a flow diagram of method steps for decomposing cubic Bèziersegments into simple cubic Bèzier path segments for tessellation-freestencil filling, according to one embodiment of the present invention.Although the method steps are described in conjunction with the systemsof FIGS. 2A, 2B, 3A, 3B, 3C, and 4, persons skilled in the art willunderstand that any system configured to perform the method steps, inany order, is within the scope of the inventions. The CPU 102 orparallel processing subsystem 112 may be configured to decompose cubicBèzier path segments into simple cubic Bèzier segments withouttessellation.

At step 805 a path segment is received by a path fill engine. The pathfill engine may be embodied as an application program, driver program,or as circuitry configured to perform the method steps shown in FIG. 8A.At step 810 the path fill engine determines if the path segment is aline, and, if so at step 815 the anchor triangle is captured beforeproceeding to step 890. Otherwise, at step 820 the path fill enginedetermines if the path segment is a quadratic Bèzier path segment, and,if so at step 825 the anchor triangle and the quadratic discard triangleis captured before proceeding to step 885.

At step 830 the path fill engine determines if the path segment is anarc, and, if so at step 835 a discard triangle fan and anchor trianglesare generated by the path fill engine before proceeding to step 885.Otherwise, the path segment is a cubic Bèzier path segment, and at step840 the cubic Bèzier path segment is classified based on the topologyand processed, as described in conjunction with FIG. 8B. At step 885 adiscard shader program is executed to render the hull geometry,discarding pixels that are not inside of the path segment and updatingthe stencil buffer. Different discard shaders are used for the differentpath segment types, e.g., arcs, quadratic Bèzier, cubic Bèzier, and thelike. At step 890 a stencil shader program is executed to render theanchor geometry to complete generation of the stencil buffer. At step895 the path segment is filled based on the stencil buffer by renderingthe bounding geometry with writes to the color buffer enabled. Thestencil buffer may be reset or cleared to its state prior to renderingthe stenciled geometry using the stencil operation during the final fillcovering step.

FIG. 8B is a flow diagram of method steps for classifying and processinga cubic path segment as performed in a method step 840 shown in FIG. 8A,according to one embodiment of the present invention. At step 845 thepath fill engine determines if the cubic Bèzier path segment isdegenerate, and, if so at step 850 a degenerate point is discarded, adegenerate line is processed as a line, and a degenerate quadratic isprocessed as a quadratic Bèzier path segment.

At step 855 the path fill engine determines if the cubic Bèzier pathsegment has a serpentine (or cusp) topology, and, if so at step 860 thepath fill engine subdivides the cubic Bèzier path segment into twosimple cubic Bèzier path segments. At step 880 the path fill enginegenerates cubic Bèzier texture coordinates for discard triangles orquadrilaterals and generates cubic Bèzier texture coordinates for anchortriangles.

If at step 855 the path fill engine determines that the cubic Bèzierpath segment does not have a serpentine topology, then the cubic Bèzierpath segment has a loop topology. A loop topology self-intersects mayhave either a single root point or a double root point, depending onwhether there are one or two intersections in the [0,1] parametric rangeof the cubic Bèzier path segment. At step 870 the path fill enginedetermines if the cubic Bèzier path segment self intersects within the[0,1] parametric range, and, if so then at step 875 the path fill enginesubdivides the cubic Bèzier path segment into two or three simple cubicBèzier path segments before proceeding to step 880. If at step 870 thepath fill engine determines that the cubic Bèzier path segment does notself-intersect within the [0,1] parametric range, then the path fillengine proceeds directly to step 880 since the cubic Bèzier path segmentis a simple cubic Bèzier path segment.

The geometry set of simple Bèzier cubic segments resulting from dividingBèzier cubic segments is resolution-independent meaning that the filledpath can be rasterized under arbitrary projective transformationswithout needing to revisit the construction of the geometry set. Thisresolution-independent property is unlike geometry sets built through aprocess of tessellating curved regions into triangles; in suchcircumstances, sufficient magnification of the filled path would revealthe tessellated underlying nature of such a tessellated geometry set.The simple Bèzier cubic segments are also compact meaning that thenumber of bytes required to represent the filled path is linear with thenumber of path segments in the original path. This property does notgenerally hold for tessellated versions of filled paths where theprocess of subdividing curved edges and introducing tessellatedtriangles typically increases the size of the resulting geometry setconsiderably.

One embodiment of the invention may be implemented as a program productfor use with a computer system. The program(s) of the program productdefine functions of the embodiments (including the methods describedherein) and can be contained on a variety of computer-readable storagemedia. Illustrative computer-readable storage media include, but are notlimited to: (i) non-writable storage media (e.g., read-only memorydevices within a computer such as CD-ROM disks readable by a CD-ROMdrive, flash memory, ROM chips or any type of solid-state non-volatilesemiconductor memory) on which information is permanently stored; and(ii) writable storage media (e.g., floppy disks within a diskette driveor hard-disk drive or any type of solid-state random-accesssemiconductor memory) on which alterable information is stored.

The invention has been described above with reference to specificembodiments. Persons skilled in the art, however, will understand thatvarious modifications and changes may be made thereto without departingfrom the broader spirit and scope of the invention as set forth in theappended claims. The foregoing description and drawings are,accordingly, to be regarded in an illustrative rather than a restrictivesense.

1. A method of decomposing cubic Bèzier path segments, the methodcomprising: receiving a path including a cubic Bèzier path segment;subdividing the cubic Bèzier path segment into simple cubic Bèzier pathsegments when the cubic Bèzier path segment is classified as having aserpentine or loop topology; assigning texture map coordinates tovertices of the simple cubic Bèzier path segments that define a convexhull geometry; and generating a stencil buffer indicating pixels thatare inside of the cubic Bèzier path segment by processing the texturemap coordinates.
 2. The method of claim 1, wherein the generating of thestencil buffer comprises processing an anchor geometry that is definedby an anchor point and a start vertex and an end vertex of a firstsimple cubic Bèzier path segment of the simple cubic Bèzier pathsegments.
 3. The method of claim 2, wherein the generating of thestencil buffer comprises incrementing values of the stencil buffercorresponding to pixels covered by the anchor geometry when the anchorgeometry is front-facing and decrementing the values of the stencilbuffer corresponding to the pixels covered by the anchor geometry whenthe anchor geometry is back-facing.
 4. The method of claim 1, whereinthe generating of the stencil buffer comprises discarding pixels coveredby the convex hull geometry based on a function of the texture mapcoordinates.
 5. The method of claim 4, wherein the generating of thestencil buffer comprises incrementing values of the stencil buffercorresponding to surviving pixels covered by the convex hull geometrywhen the convex hull geometry is front-facing and decrementing thevalues of the stencil buffer corresponding to the surviving pixelscovered by the convex hull geometry when the convex hull geometry isback-facing.
 6. The method of claim 1, further comprising replacing adegenerate cubic Bèzier path segment of the path with a quadratic Bèzierpath segment, a line segment, or a point.
 7. The method of claim 1,wherein the generating of the stencil buffer comprises disabling writesto a depth buffer and a color buffer.
 8. The method of claim 1, furthercomprising: constructing a bounding geometry that encloses the path; andrendering the bounding geometry and writing the color buffer based onthe stencil buffer to fill pixels that are inside of the path.
 9. Themethod of claim 1, wherein the subdividing of the cubic Bèzier pathsegment comprises dividing the cubic Bèzier path segment having a looptopology into a first simple cubic Bèzier path segment and a secondsimple cubic Bèzier path segment at a root point.
 10. The method ofclaim 1, wherein the subdividing of the cubic Bèzier path segmentcomprises dividing the cubic Bèzier path segment having a serpentinetopology into a first simple cubic Bèzier path segment and a secondsimple cubic Bèzier path segment at an intersection point of the cubicBèzier path segment and a base segment between a start vertex and an endvertex of the cubic Bèzier path segment.
 11. A non-transitorycomputer-readable storage medium storing instructions that, whenexecuted by a processor, cause the processor to decompose cubic Bèzierpath segments, by performing the steps of: receiving a path including acubic Bèzier path segment; subdividing the cubic Bèzier path segmentinto simple cubic Bèzier path segments when the cubic Bèzier pathsegment is classified as having a serpentine or loop topology; assigningtexture map coordinates to vertices of the simple cubic Bèzier pathsegments that define a convex hull geometry; and generating a stencilbuffer indicating pixels that are inside of the cubic Bèzier pathsegment by processing the texture map coordinates.
 12. Thenon-transitory computer-readable storage medium of claim 11, wherein thegenerating of the stencil buffer comprises processing an anchor geometrythat is defined by an anchor point and a start vertex and an end vertexof a first simple cubic Bèzier path segment of the simple cubic Bèzierpath segments.
 13. The non-transitory computer-readable storage mediumof claim 12, wherein the generating of the stencil buffer comprisesincrementing values of the stencil buffer corresponding to pixelscovered by the anchor geometry when the anchor geometry is front-facingand decrementing the values of the stencil buffer corresponding to thepixels covered by the anchor geometry when the anchor geometry isback-facing.
 14. The non-transitory computer-readable storage medium ofclaim 11, wherein the generating of the stencil buffer comprisesdiscarding pixels covered by the convex hull geometry based on afunction of the texture map coordinates.
 15. The non-transitorycomputer-readable storage medium of claim 14, wherein the generating ofthe stencil buffer comprises incrementing values of the stencil buffercorresponding to surviving pixels covered by the convex hull geometrywhen the convex hull geometry is front-facing and decrementing thevalues of the stencil buffer corresponding to the surviving pixelscovered by the convex hull geometry when the convex hull geometry isback-facing.
 16. The non-transitory computer-readable storage medium ofclaim 11, further comprising replacing a degenerate cubic Bèzier pathsegment of the path with a quadratic Bèzier path segment, a linesegment, or a point.
 17. The non-transitory computer-readable storagemedium of claim 11, further comprising: constructing a bounding geometrythat encloses the path; and rendering the bounding geometry and writingthe color buffer based on the stencil buffer to fill pixels that areinside of the path.
 18. The non-transitory computer-readable storagemedium of claim 11, wherein the subdividing of the cubic Bèzier pathsegment comprises dividing the cubic Bèzier path segment having a looptopology into a first simple cubic Bèzier path segment and a secondsimple cubic Bèzier path segment at a root point.
 19. The non-transitorycomputer-readable storage medium of claim 11, wherein the subdividing ofthe cubic Bèzier path segment comprises dividing the cubic Bèzier pathsegment having a serpentine topology into a first simple cubic Bèzierpath segment and a second simple cubic Bèzier path segment at anintersection point of the cubic Bèzier path segment and a base segmentbetween a start vertex and an end vertex of the cubic Bèzier pathsegment.
 20. A system for decomposing cubic Bèzier path segments, thesystem comprising: a memory that is configured to store a stencilbuffer; and a processor that is coupled to the memory and configured to:receive a path including a cubic Bèzier path segment; subdivide thecubic Bèzier path segment into simple cubic Bèzier path segments whenthe cubic Bèzier path segment is classified as having a serpentine orloop topology; assign texture map coordinates to vertices of the simplecubic Bèzier path segments that define a convex hull geometry; and writevalues to the stencil buffer indicating pixels that are inside of thecubic Bèzier path segment by processing the texture map coordinates.